A path of uniform width surrounds a circular park. The difference of internal and external circumference of this circular path is 132 metres. Its width is :
(Take `pi = (22)/(7)`)

Options

A. 22m
B. 20 m
C. 21m
D. 24m

Answer

To find the width of the path surrounding the circular park, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a circular park surrounded by a path of uniform width. The difference between the external circumference (the circumference of the park plus the path) and the internal circumference (the circumference of just the park) is given as 132 meters.

2. **Formulate the Circumference**:
- Let the radius of the circular park be \( r \) meters.
- The width of the path is \( w \) meters.
- The internal circumference (C1) of the park is given by:
\[ C_1 = 2\pi r \]
- The external circumference (C2) of the park plus the path is:
\[ C_2 = 2\pi (r + w) = 2\pi r + 2\pi w \]

3. **Set Up the Equation**:
- The difference between the external and internal circumference is:
\[ C_2 - C_1 = 2\pi w \]
- According to the problem, this difference is 132 meters:
\[ 2\pi w = 132 \]

4. **Substituting the Value of \(\pi\)**:
- We are given that \(\pi = \frac{22}{7}\). Substituting this into the equation gives:
\[ 2 \times \frac{22}{7} \times w = 132 \]

5. **Simplifying the Equation**:
- Multiply both sides by 7 to eliminate the fraction:
\[ 2 \times 22 \times w = 132 \times 7 \]
- This simplifies to:
\[ 44w = 924 \]

6. **Solving for Width \(w\)**:
- Divide both sides by 44:
\[ w = \frac{924}{44} \]
- Simplifying this gives:
\[ w = 21 \]

### Final Answer:
The width of the path is **21 meters**.